A VLSI Array Architecture for Realization of DFT, DHT, DCT and DST

A unified array architecture is described for computation of DFT, DHT, DCT and DST using a modified CORDIC (CoOrdinate Rotation DIgital Computer) arithmetic unit as the basic Processing Element (PE). All these four transforms can be computed by simple rearrangement of input samples. Compared to five other existing architectures, this one has the advantage in speed in terms of latency and throughput. Moreover, the simple local neighborhood interprocessor connections make it convenient for VLSI implementation. The architecture can be extended to compute transformation of longer length by judicially cascading the modules of shorter transformation length which will be suitable for Wafer Scale Integration (WSI). CORDIC is designed using Transmission Gate Logic (TGL) on sea of gates semicustom environment. Simulation results show that this architecture may be a suitable candidate for low power/low voltage applications

Performance Analysis and Design of a Discreet Cosine Transform processor Using CORDIC algorithm

CORDIC is an acronym for COrdinate Rotation Digital Computer. It is a class of shift adds algorithms for rotating vectors in a plane, which is usually used for the calculation of trigonometric functions, multiplication, division and conversion between binary and mixed radix number systems of DSP applications, such as Discreet cosine Transform(DCT). The Jack E. Volder's CORDIC algorithm is derived from the general equations for vector rotation. The CORDIC algorithm has become a widely used approach to elementary function evaluation when the silicon area is a primary constraint. The implementation of CORDIC algorithm requires less complex hardware than the conventional method. In digital communication, the straightforward evaluation of the cited functions is important, numerous matrix based adaptive signal processing algorithms require the solution of systems of linear equations, the computation of eigen values, eigenvectors or singular values. All these tasks can be efficiently implemented using processing elements performing vector rotations. The (CORDIC) offers the opportunity to calculate all the desired functions in a rather simple and elegant way. Due to the simplicity of the involved operations the CORDIC algorithm is very well suited for VLSI implementation. The rotated vector is also scaled making a scale factor correction necessary. VHDL coding and simulation of selected CORDIC algorithm for sine and cosine, the comparison of resultant implementations and the specifics of the FPGA implementation has been discussed. In this thesis, the CORDIC algorithm has been implemented in XILINX Spartan 3E FPGA kit using VHDL and is found to be accurate. It also contains the implementation of Discrete Cosine Transform using radix-2 decimation-in-time algorithm in Xilinx. on the same FPGA kit. Due to the high speed, low cost and greater flexibility offered by FPGAs over DSP processors the FPGA based computing is becoming the heart of all digital signal processing systems of modern era. Moreover the generation of test bench by Xilinx ISE 9.2i verifies the results with directly computed dct values from mat lab

A CORDIC like processor for computation of arctangent and absolute magnitude of a vector

In this paper, we propose a CORDIC like algorithm for computing absolute magnitude of a vector and its corresponding phase angle. It eliminates scale factor compensation step as well as the addition/subtraction operation along the z datapath. The synthesis result shows that the proposed processor is hardware economic and suitable for low power applications

A 16-bit CORDIC rotator for high-performance wireless LAN

In this paper we propose a novel 16-bit low power CORDIC rotator that is used for high-speed wireless LAN. The algorithm converges to the final target angle by adaptively selecting appropriate iteration steps while keeping the scale factor virtually constant. The VLSI architecture of the proposed design eliminates the entire arithmetic hardware in the angle approximation datapath and reduces the number of iterations by 50% on an average. The cell area of the processor is 0.7 mm2 and it dissipates 7 mW power at 20 MHz frequency

Signal processing applications of massively parallel charge domain computing devices

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array

Design of digital IP block for discrete cosine transform

Tato diplomová práce se zabývá návrhem IP bloku pro diskrétní kosinovou transformaci. V~teoretické části jsou shrnuty algoritmy pro výpočet diskrétní kosinové transformace a diskutována jejich použitelnost v~hardwaru. Zvolený algoritmus pro hardwarovou implementaci je modelován v jazyce C. Poté je popsán na RTL úrovni, verifikován a je provedena syntéza v~technologii TSMC 65 nm. Hardwarová implementace je poté zhodnocena s ohledem na datovou propustnost, plochu, rychlost and spotřebu.This diploma thesis deals with design of IP block for discrete cosine transform. Theoretical part summarizes algorithms for computation of discrete cosine transform and their hardware usability is discussed. Chosen algorithm for hardware implementation is modeled in C language. Algorithm is described at RTL level, verified and synthesized to TSMC 65 nm technology. Hardware implementation is then evaluated with respect of throughput, area, speed and power consumption.

Efficient VLSI Architectures for Image Compression Algorithms

An image, in its original form, contains huge amount of data which demands not only large amount of memory requirements for its storage but also causes inconvenient transmission over limited bandwidth channel. Image compression reduces the data from the image in either lossless or lossy way. While lossless image compression retrieves the original image data completely, it provides very low compression. Lossy compression techniques compress the image data in variable amount depending on the quality of image required for its use in particular application area. It is performed in steps such as image transformation, quantization and entropy coding. JPEG is one of the most used image compression standard which uses discrete cosine transform (DCT) to transform the image from spatial to frequency domain. An image contains low visual information in its high frequencies for which heavy quantization can be done in order to reduce the size in the transformed representation. Entropy coding follows to further reduce the redundancy in the transformed and quantized image data. Real-time data processing requires high speed which makes dedicated hardware implementation most preferred choice. The hardware of a system is favored by its lowcost and low-power implementation. These two factors are also the most important requirements for the portable devices running on battery such as digital camera. Image transform requires very high computations and complete image compression system is realized through various intermediate steps between transform and final bit-streams. Intermediate stages require memory to store intermediate results. The cost and power of the design can be reduced both in efficient implementation of transforms and reduction/removal of intermediate stages by employing different techniques. The proposed research work is focused on the efficient hardware implementation of transform based image compression algorithms by optimizing the architecture of the system. Distribute arithmetic (DA) is an efficient approach to implement digital signal processing algorithms. DA is realized by two different ways, one through storage of precomputed values in ROMs and another without ROM requirements. ROM free DA is more efficient. For the image transform, architectures of one dimensional discrete Hartley transform (1-D DHT) and one dimensional DCT (1-D DCT) have been optimized using ROM free DA technique. Further, 2-D separable DHT (SDHT) and 2-D DCT architectures have been implemented in row-column approach using two 1-D DHT and two 1-D DCT respectively. A finite state machine (FSM) based architecture from DCT to quantization has been proposed using the modified quantization matrix in JPEG image compression which requires no memory in storage of quantization table and DCT coefficients. In addition, quantization is realized without use of multipliers that require more area and are power hungry. For the entropy encoding, Huffman coding is hardware efficient than arithmetic coding. The use of Huffman code table further simplifies the implementation. The strategies have been used for the significant reduction of memory bits in storage of Huffman code table and the complete Huffman coding architecture encodes the transformed coefficients one bit per clock cycle. Direct implementation algorithm of DCT has the advantage that it is free of transposition memory to store intermediate 1-D DCT. Although recursive algorithms have been a preferred method, these algorithms have low accuracy resulting in image quality degradation. A non-recursive equation for the direct computation of DCT coefficients have been proposed and implemented in both 0.18 µm ASIC library as well as FPGA. It can compute DCT coefficients in any order and all intermediate computations are free of fractions and hence very high image quality has been obtained in terms of PSNR. In addition, one multiplier and one register bit-width need to be changed for increasing the accuracy resulting in very low hardware overhead. The architecture implementation has been done to obtain zig-zag ordered DCT coefficients. The comparison results show that this implementation has less area in terms of gate counts and less power consumption than the existing DCT implementations. Using this architecture, the complete JPEG image compression system has been implemented which has Huffman coding module, one multiplier and one register as the only additional modules. The intermediate stages (DCT to Huffman encoding) are free of memory, hence efficient architecture is obtained

Orthogonal transforms in digital image coding.

by Lo Kwok Tung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1989.Bibliography: leaves [71-74